A current challenge in condensed matter physics is the search for novel quantum states of matter. In this paper, the authors provide a simple guiding principle for finding quantum spin liquids in real materials. Like in the case of unconventional superconductivity that involves pairing of two fermions into a bound state, it is shown here that chiral quantum liquids naturally emerge in the vicinity of a class of magnetic quantum critical points, due to pairing of two bosons into a bound state of zero total spin.A current challenge in condensed matter physics is the search for novel quantum states of matter. In this paper, the authors provide a simple guiding principle for finding quantum spin liquids in real materials. Like in the case of unconventional superconductivity that involves pairing of two fermions into a bound state, it is shown here that chiral quantum liquids naturally emerge in the vicinity of a class of magnetic quantum critical points, due to pairing of two bosons into a bound state of zero total spin.

arXiv:1708.02980Physical review. B./Physical review. BNov 7, 201719 citations

Magnetic-flux tuning of spin chirality in Mott insulators with ring exchanges

Yi-Fei Wang, Chang-De Gong

A peculiar manifestation of the Aharonov-Bohm effect in Mott insulators, presents as a versatile scheme to manipulate the intriguing ground-state spin chirality, such as, tune the magnitude continuously, switch an abrupt jump, or even reverse its sign from a para-chiral phase to a dia-chiral phase. Such an unusual mechanism is due to the coupling between multiple-spin ring exchanges and magnetic flux, and the competition between spin chirality and magnetism, and is demonstrated explicitly in both quasi-one-dimensional ladders and two-dimensional lattices with triangles as elementary plaquettes.A peculiar manifestation of the Aharonov-Bohm effect in Mott insulators, presents as a versatile scheme to manipulate the intriguing ground-state spin chirality, such as, tune the magnitude continuously, switch an abrupt jump, or even reverse its sign from a para-chiral phase to a dia-chiral phase. Such an unusual mechanism is due to the coupling between multiple-spin ring exchanges and magnetic flux, and the competition between spin chirality and magnetism, and is demonstrated explicitly in both quasi-one-dimensional ladders and two-dimensional lattices with triangles as elementary plaquettes.

arXiv:0909.1622Physical Review BOct 27, 20101 citation

Exotic quantum phases in two-dimensional frustrated magnets

Jason Alicea

Dec 1, 20070 citations

GAPLESS CHIRALITY EXCITATIONS IN ONE-DIMENSIONAL SPIN-1/2 FRUSTRATED MAGNETS

Shunsuke Furukawa, Masahiro Sato, Yasuhiro Saiga +1 more

Foundations of Quantum Mechanics in the Light of New TechnologyJun 1, 20090 citations

Emergent quasi-one-dimensionality in a kagome magnet: A simple route to complexity

Shou-Shu Gong, Wei Kang Zhu, Kun Yang +3 more

We study the ground-state phase diagram of the quantum $\text{spin-}1/2$ Heisenberg model on the kagome lattice with first- $({J}_{1}<0)$ , second- $({J}_{2}<0)$ , and third-neighbor interactions $({J}_{d}>0)$ by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the ${J}_{d}\text{-dominant}$ regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions ${J}_{1,2}$ . When either ${J}_{1}$ or ${J}_{2}$ is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.We study the ground-state phase diagram of the quantum $\text{spin-}1/2$ Heisenberg model on the kagome lattice with first- $({J}_{1}<0)$, second- $({J}_{2}<0)$, and third-neighbor interactions $({J}_{d}>0)$ by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the ${J}_{d}\text{-dominant}$ regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions ${J}_{1,2}$. When either ${J}_{1}$ or ${J}_{2}$ is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.

arXiv:1604.01459Physical review. B./Physical review. BJul 27, 201627 citations

We study the ground-state phase diagram of the quantum

\text{spin-}1/2

Heisenberg model on the kagome lattice with first-

({J}_{1}<0)

, second-

({J}_{2}<0)

, and third-neighbor interactions

({J}_{d}>0)

by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the

{J}_{d}\text{-dominant}

regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions

{J}_{1,2}

. When either

{J}_{1}

{J}_{2}

is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.